login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117444 Period 5: Repeat [0, 1, 2, -2, -1]. 9
0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See the comments in A203571 concerning formulas of the n-th term of periodic sequences. - M. F. Hasler, Jan 13 2013

LINKS

Table of n, a(n) for n=0..75.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1)

FORMULA

G.f.: x(1+3x+x^2)/(1+x+x^2+x^3+x^4) = x(1+2x^2-2x^3-x^4)/(1-x^5).

a(n) = sum{k=0..5, L(k(k^2-n)/5)}/2, where L(j/p) is the Legendre symbol of j and p.

a(n) = sqrt(2+2/sqrt(5))*sin(2*Pi*n/5)-sqrt(2-2/sqrt(5))*sin(4*Pi*n/5).

a(n) = -(1/5)*{(n mod 5)+[(n+1) mod 5]-4*[(n+2) mod 5]+[(n+3) mod 5]+[(n+4) mod 5]}, with n>=0. - Paolo P. Lava, Jun 11 2007

a(n) = -2 + floor(23401/99999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013

a(n) = -2 + floor(863/1562*5^(n+1)) mod 5. - Hieronymus Fischer, Jan 04 2013

a(n) = 2 - ((2-n) mod 5). - Wesley Ivan Hurt, Jul 12 2014

MAPLE

A117444:=n->2 - ((2-n) mod 5): seq(A117444(n), n=0..50); # Wesley Ivan Hurt, Jul 12 2014

MATHEMATICA

Table[2 - Mod[2 - n, 5], {n, 0, 50}] (* Wesley Ivan Hurt, Jul 12 2014 *)

PROG

(PARI) A117444(n)=4315*5^(n%5)\1562%5-2  \\ M. F. Hasler, Jan 13 2013

(PARI) A117444(n, p=[0, 1, 2, -2, -1])=p[n%#p+1] \\ M. F. Hasler, Jan 13 2013

(MAGMA) [2-((2-n) mod 5) : n in [0..50]]; // Wesley Ivan Hurt, Jul 12 2014

CROSSREFS

Cf. A061347.

Sequence in context: A180424 A092339 A079693 * A257145 A253262 A015504

Adjacent sequences:  A117441 A117442 A117443 * A117445 A117446 A117447

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 16 2006

EXTENSIONS

More terms from Wesley Ivan Hurt, Jul 12 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)